I believe it is for flutter suppression considerations. The heavier missile with cg forward of wing twist axis, helps to suppress flutter bettsr. Before AMRAAM, the AIM-9 on the tip was better for flutter suppression than a clean tip.

Like johnwill said, it is an improvised aeroelastic feature intended to avoid what's called "flexure-torsion binary flutter" by keeping the CG of the wing forward of the twist axis. AMRAAM is longer and heavier and therefore when loaded it better shifts the CG forward of said axis than, say, a sidewinder.

Also, there is a lower Drag Index (DI) with the AIM-120s on the wingtips, believe it or not. Also, if you load 6 air to air missiles, the DI is much lower with the AIM-120s on the outboard stations (1,2,8,9) and the AIM-9s on 3 and 7. Lots of guys with 50 pound brains figuring it out. On a side note, the jet is faster (less drag) with 2 x MK84s vs. 6x MK82s.